Socratic-Generator-32B: Adaptive Data Generation

• Socratic-Generator-32B is a multi-agent LLM framework characterized by autonomous curriculum evolution and iterative data synthesis.
• It leverages a co-evolutionary loop among Teacher, Solver, and Generator to refine problem sets and address model weaknesses.
• Empirical results show improved mathematical reasoning with a +20.2% accuracy gain and 95.6% data validity in generated training samples.

Socratic-Generator-32B denotes a class of LLM architectures and data generation frameworks aimed at synthesizing high-quality reasoning and educational data via automated, curriculum-adaptive, and multi-agent Socratic dialogue. The approach is distinct in leveraging an autonomous, iterative process—rooted in the co-evolution of interacting agent roles such as Teacher, Solver, and Generator—to address the data bottlenecks in mathematical and code reasoning domains. Socratic-Generator-32B extends beyond classical pedagogical Socratic methods by formalizing agent-based data generation and validation cycles that enable the scalable, self-improving creation of challenging problem-answer pairs suitable for fine-tuning high-performance student LLMs. The framework is evaluated on stringent mathematical reasoning benchmarks and shows superior data validity and end-task effectiveness compared to previous static or distillation-based synthesis methods, even outperforming larger commercial LLMs on key metrics (Wang et al., 29 Sep 2025).

1. Autonomous Agent-Based Curriculum Evolution

The Socratic-Generator-32B paradigm is instantiated through a co-evolutionary multi-agent loop, inspired by the classical Socratic method yet formalized for LLMs:

• Teacher: A fixed, expert LLM (e.g., a large proprietary or open-source LM) that serves as both verifier (evaluating solutions) and refiner (modifying or generating curriculum items focused on revealed weaknesses).
• Solver: A trainable LLM that attempts problem solutions, receives preference-based feedback, and incrementally improves its reasoning ability via preference optimization losses such as Direct Preference Optimization (DPO).
• Generator: An agent that learns the Teacher's curriculum design and problem refinement heuristics through weighted supervised fine-tuning (WSFT), enabling scalable and efficient generation of new, high-value training data.

The procedure forms a closed loop: the Solver attempts problems, failures are identified and classified by the Teacher, and the Generator then synthesizes refined or more challenging problems that target specific weaknesses in the Solver's current performance profile. The resulting self-evolving curriculum is continually updated to ensure the problem set remains at an optimal zone of proximal development for the Solver (Wang et al., 29 Sep 2025).

2. Data Generation and Problem Refinement Mechanism

Socratic-Generator-32B is initialized from a minimal set of human- or LLM-generated seed problems (e.g., 100 exemplars). The data pipeline proceeds as follows:

1. The Solver generates solution trajectories for a set of problems.
2. Solution attempts are partitioned into “winning” and “losing” sets via the Teacher's verification function $V(q, y)$, where $q$ is the question and $y$ a candidate solution.
3. For failed cases, the Teacher applies a problem refinement operator $G(q, y_{\text{fail}})$, yielding a new problem and reference solution targeting the specific error or gap exposed by the Solver.
4. The curriculum $\mathcal{D}_{t}$ is augmented:

$$\mathcal{D}_{t+1} = \mathcal{D}_t \cup \{ G(q, y_{\text{fail}}):(q, y_{\text{fail}})\in \text{failures} \}$$

Problems are utility-weighted using a Gaussian function: $$U(q' | \pi_{\theta_S}) = \exp\left(-\frac{(s_{q'} - \mu)^2}{2\sigma^2}\right)$$ where $s_{q'}$ is a scalar score reflecting challenge level, and typical parameters are $\mu = 0.5, \sigma = 0.2$, consistent with curriculum learning principles targeting problems of neither trivial nor excessive difficulty (Wang et al., 29 Sep 2025).

This data-centric, preference-driven refinement eliminates reliance on large-scale human annotation or static distillation, resulting in a high-validity problem set (e.g., 95.6% solvability by the Teacher agent).

3. Performance Metrics and Empirical Validation

Empirical studies reported in (Wang et al., 29 Sep 2025) demonstrate the effectiveness of Socratic-Generator-32B as a data generator for mathematical reasoning LLMs:

• Downstream Model Training: Using synthetic data from Socratic-Generator-32B, student LLMs such as DeepSeek-R1-Distill-Llama-8B achieve average benchmark accuracy scores of 37.72% across comprehensive targets such as AMC23, AIME24-25, Olympiad, MATH-500, Minerva, and GSM8K.
• Relative Gains: This training regime yields a +20.2 percentage point average increase in accuracy over static, non-adaptive data generation methods under identical settings.
• Comparisons to SOTA: Student LLMs fine-tuned with Socratic-Generator-32B data match or surpass the performance of student LLMs trained on data from teacher models (e.g., Qwen3-235B), sometimes marginally exceeding the latter’s accuracy.

Data validity rates (i.e., the fraction of generated problems for which a powerful teacher LLM can produce a solution) consistently reach around 95.6% in experimental evaluations.

4. Technical Innovations

Several innovations differentiate Socratic-Generator-32B from prior approaches:

• Co-Evolutionary Multi-Agent Architecture: The tightly coupled interaction between Teacher, Solver, and Generator creates a dynamic, self-improving data ecosystem.
• Preference-Based Curriculum Adaptation: The system leverages preference learning (DPO) to optimize the Solver’s learning trajectory, directly aligning problem generation with observed weaknesses rather than generic distributions.
• WSFT for Generator Training: The Generator distills the Teacher’s sophisticated problem refinement strategies, allowing the system to scale high-fidelity data synthesis without continually invoking costly large models.
• Online, Self-Generating Curriculum: The process is fully automated and requires no ongoing human curation or annotation after the initial seed set.

This architecture addresses core limitations in previous synthetic data generation: lack of adaptation, limited challenge targeting, and the inability to dynamically track and remedy evolving model weaknesses.

5. Implications for LLM Training and Educational Utility

Socratic-Generator-32B demonstrates that high-quality reasoning data can be autonomously synthesized from a small seed set, enabling robust student LLM training without dependence on massive human annotation or proprietary teacher models. The paradigm exhibits several implications:

• Greater Data Efficiency: The co-evolutionary loop rapidly exposes and corrects model blind spots, ensuring that data synthesis targets only zones of greatest learning potential.
• Improved Generalization: Student LLMs trained on Socratic-Generator-32B output not only solve benchmark mathematical problems at high accuracy, but also display improved robustness to novel reasoning scenarios compared to those trained with traditional static or distillation datasets.
• Potential for Domain Expansion: While the empirical results in (Wang et al., 29 Sep 2025) focus on mathematical reasoning, the same autonomous curriculum loop is plausibly extensible to domains such as formal logic, coding, physical sciences, and other structured reasoning contexts.
• Reduced Reliance on Human-Labeled Data: The closed-loop, data-free generation model offers a scalable template for domains where annotated data is scarce or rapidly outdated.

This approach paves the way for research into adaptive, self-improving training regimes that can dynamically keep pace with both model and domain evolution.

6. Comparative Position and Future Directions

Socratic-Generator-32B outperforms both traditional data synthesis and static distillation approaches according to extensive benchmark results (Wang et al., 29 Sep 2025). Its fully autonomous and preference-adaptive data generation loop is unique in current literature. Promising directions for future research, directly supported by findings in (Wang et al., 29 Sep 2025), include:

• Application of the multi-agent preference-based curriculum loop to broader content domains beyond mathematics,
• Integration with more granular, multi-step feedback (e.g., intermediate reasoning validation, decomposed explanations),
• Exploration of continual learning scenarios where the curriculum dynamically adjusts to new problem archetypes or task requirements as the underlying model or its deployment goals evolve.

The paradigm of Socratic-Generator-32B represents a shift in LLM data generation: from passive or static pattern reproduction to a model-driven, closed-loop, epistemically grounded process where challenge, verification, and refinement are all enacted by autonomous, interacting agents, thereby yielding higher-fidelity and more effective training signals for next-generation reasoning tasks.